#12876: Fix element and parent classes of Hom categories to be abstract, and
simplify the Hom logic.
------------------------------------------+---------------------------------
       Reporter:  nthiery                 |         Owner:  nthiery             
      
           Type:  enhancement             |        Status:  needs_review        
      
       Priority:  major                   |     Milestone:  sage-5.4            
      
      Component:  categories              |    Resolution:                      
      
       Keywords:  categories, Hom         |   Work issues:  fix doctests and 
segfaults
Report Upstream:  N/A                     |     Reviewers:  Simon King          
      
        Authors:  Nicolas M. ThiƩry       |     Merged in:                      
      
   Dependencies:  #11521, #12215, #12313  |      Stopgaps:                      
      
------------------------------------------+---------------------------------

Comment (by nthiery):

 Hi Simon!

 Replying to [comment:62 SimonKing]:
 > I think implementing a `_an_element_` is easy enough that I can do it in
 another reviewer patch. One thing doesn't work as described in the
 documentation, though. It says that a homomorphism of Hecke algebras can
 not only be obtained from a matrix (that works) but from an element of a
 Hecke algebra (I suppose: An element of the codomain). However, this isn't
 implemented.
 >
 > I am not competent to implement it. So, I suggest that I start with
 implementing `_an_element_`, try to use the category framework on these
 homsets (i.e., define the Element attribute), and very important: Make the
 homsets unique upon pickling. Namely:
 > {{{
 > sage: M = ModularForms(Gamma0(7), 4)
 > sage: H = Hom(M,M)
 > sage: H is loads(dumps(H))
 > False
 > }}}
 > so that by consequence several tests from the test suite fail.

 Feel free to just skip the failing tests and mention them, say on #12879.

 And thanks a lot for all the work you put in rebasing/finalizing this
 patch! I'll try to look at it tomorrow.

 Cheers,
                          Nicolas

-- 
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/12876#comment:64>
Sage <http://www.sagemath.org>
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